Question

A sample consisting of 2 moles He is expanded isothermally at 0 degrees from 5.0dm3 to 20.0dm3. Calculate w, q and deltaU for each of the following situations: (i) A reversible expansion of the sample. (ii) An irreversible expansion of the sample against a constant external pressure equal to the final pressure of the gas. (iii) A free expansion (against zero external pressure i.e. in a vacuum) of the sample.

Answer 1

Answer:

i) $\Delta U=0 w=-6293 J q=6293 J$

ii) $\Delta U=0 w=-3404,52 J q=3404,52 J$

ii) $\Delta U=0 w=0 J q=0 J$

Explanation:

As the initial and final states of the sample are the same, the ΔU of the sample is, for the three cases

$\Delta U=n.C_{V}.\Delta T=0$ since $\Delta T=0$

i)Reversibly $P_{ext} =P_{sys}$ so $w$ can be calculated by  

$w=-n.R.T.ln(\frac{V_{f}}{V_{i}})=-2 \times 8.314\frac{J}{mol K} \times 273,15K \times ln(\frac{}{5dm^{3}})=-6293 J$

and because of the first law of thermodynamics

$q=-w=6293 J$

ii)Irreversibly with $P_{ext} =P_{f}$

we can calculate $P_{f}$ by the law of ideal gases

$P_{f} =\frac{n\times R\times T}{V_{f}} =\frac{2\times 0.082\frac{dm^{3}atm}{mol K}\times 273,15K}{20dm^{3}} =2,24 atm$

then w can be calculated by

$w=-P_{ext} \times \Delta V=-2,24 atm \times (20-5) dm^{3} \times frac{101.325J }{atm dm^{3}=-3404,52J$

and  

$q=-w=3404,52J$

iii)a free expansion $P_{ext}$ so $w=0$ (there's no work at vaccum) and $q=-w=0$